The visitors put up a decent fight without ever threatening to cause an upset at the Withdean Stadium.
They were still in contention until midway through the second half, when Alex Revell's header doubled Brighton's lead and they easily avoided a repeat of Northwich Victoria's 8-0 drubbing at the Withdean in the previous round.
Stafford started well enough but they were punished in the 18th minute when they stood off Dean Hammond.
A headed clearance by Wayne Daniel fell to the Brighton captain 20 yards out and he had time and room to pick his spot.
Rangers keeper Danny Alcock was furious with his defenders as Hammond curled a right-foot effort beyond his despairing dive for his sixth goal of the season.
Jake Robinson's pace caused Stafford problems in the first half, but Brighton had to wait until the 66th minute to put the game beyond the underdogs.
A cross from the left by young full-back Sam Rents was met by Revell with a firm, downward header for his eighth of the campaign.
Stafford had their best chance of the match immediately afterwards, Guy Madjo almost capitalising on sloppy defending with a shot just over the crossbar.
That would have made for an interesting finish, but Jake Robinson rounded off a comfortable victory for the Seagulls in the final minute.
He latched on to a clever through-ball from Dean Cox to slot home his 12th of the season.
They were still in contention until midway through the second half, when Alex Revell's header doubled Brighton's lead and they easily avoided a repeat of Northwich Victoria's 8-0 drubbing at the Withdean in the previous round.
Stafford started well enough but they were punished in the 18th minute when they stood off Dean Hammond.
A headed clearance by Wayne Daniel fell to the Brighton captain 20 yards out and he had time and room to pick his spot.
Rangers keeper Danny Alcock was furious with his defenders as Hammond curled a right-foot effort beyond his despairing dive for his sixth goal of the season.
Jake Robinson's pace caused Stafford problems in the first half, but Brighton had to wait until the 66th minute to put the game beyond the underdogs.
A cross from the left by young full-back Sam Rents was met by Revell with a firm, downward header for his eighth of the campaign.
Stafford had their best chance of the match immediately afterwards, Guy Madjo almost capitalising on sloppy defending with a shot just over the crossbar.
That would have made for an interesting finish, but Jake Robinson rounded off a comfortable victory for the Seagulls in the final minute.
He latched on to a clever through-ball from Dean Cox to slot home his 12th of the season.